Approximate Bayes model selection procedures for Gibbs-Markov random fields
Markov random fields (MRFs) were originally introduced as models in statistical mechanics during the early 1990s. This work is motivated by texture synthesis: For an image consisting of a single texture with no degradation, we seek to choose a model from a collection of MRFs which produces typical samples resembling real textures. Since the likelihood for MRFs may be written as an exponential family, we take an approach similar to that of \textit{G. Schwarz} [Ann. Stat. 6, 461-464 (1978; Zbl 0379.62005)] to derive approximate Bayesian information criteria (BIC) for choosing a ``best'' model. In Section 2 we give a brief introduction to random fields, a Bayesian formulation of the model selection problem, and our main results. Section 3 is devoted to the likelihood and Markov chain Monte Carlo likelihood, which are basic elements in our solution to the model selection problem. In Section 4, we present a small simulation study of our results. All technical proofs are kept in Section 5.
approximate Bayesian information criteria
scientific article; zbMATH DE number 906643
scientific article